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The multi-player nonzero-sum Dynkin game in discrete time

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  • Said Hamadène
  • Mohammed Hassani

Abstract

We study the infinite horizon discrete time N-player nonzero-sum Dynkin game ( $$N \ge 2$$ N ≥ 2 ) with stopping times as strategies (or pure strategies). The payoff depends on the set of players that stop at the termination stage (where the termination stage is the minimal stage in which at least one player stops). We prove existence of a Nash equilibrium point for the game provided that, for each player $$\pi _i$$ π i and each nonempty subset $$S$$ S of players that does not contain $$\pi _i$$ π i , the payoff if $$S$$ S stops at a given time is at least the payoff if $$S$$ S and $$\pi _i$$ π i stop at that time. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Said Hamadène & Mohammed Hassani, 2014. "The multi-player nonzero-sum Dynkin game in discrete time," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 79(2), pages 179-194, April.
    • Handle: RePEc:spr:mathme:v:79:y:2014:i:2:p:179-194
    DOI: 10.1007/s00186-013-0458-1
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    References listed on IDEAS

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    1. Rida Laraki & Eilon Solan, 2002. "Stopping Games in Continuous Time," Discussion Papers 1354, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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    Cited by:

    1. Ivan Guo & Marek Rutkowski, 2017. "Arbitrage-free pricing of multi-person game claims in discrete time," Finance and Stochastics, Springer, vol. 21(1), pages 111-155, January.
    2. Miryana Grigorova & Marie-Claire Quenez, 2017. "Optimal stopping and a non-zero-sum Dynkin game in discrete time with risk measures induced by BSDEs," Papers 1705.03724, arXiv.org.
    3. Miryana Grigorova & Marie-Claire Quenez & Yuan Peng, 2023. "Non-linear non-zero-sum Dynkin games with Bermudan strategies," Papers 2311.01086, arXiv.org.
    4. Steg, Jan-Henrik, 2015. "Symmetric equilibria in stochastic timing games," Center for Mathematical Economics Working Papers 543, Center for Mathematical Economics, Bielefeld University.
    5. de Angelis, Tiziano & Ferrari, Giorgio & Moriarty, John, 2016. "Nash equilibria of threshold type for two-player nonzero-sum games of stopping," Center for Mathematical Economics Working Papers 563, Center for Mathematical Economics, Bielefeld University.
    6. Riedel, Frank & Steg, Jan-Henrik, 2017. "Subgame-perfect equilibria in stochastic timing games," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 36-50.
    7. Erhan Bayraktar & Song Yao, 2015. "On the Robust Dynkin Game," Papers 1506.09184, arXiv.org, revised Sep 2016.
    8. Miryana Grigorova & Marie-Claire Quenez, 2017. "Optimal stopping and a non-zero-sum Dynkin game in discrete time with risk measures induced by BSDEs," Post-Print hal-01519215, HAL.
    9. Guo, Ivan & Rutkowski, Marek, 2016. "Discrete time stochastic multi-player competitive games with affine payoffs," Stochastic Processes and their Applications, Elsevier, vol. 126(1), pages 1-32.

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